On a functional differential equation

© 2017, Pleiades Publishing, Ltd.Conditions for the existence and uniqueness of a solution to a problem for a functional differential equation are presented. A special case of this equation is a functional differential equation derived previously by the authors for the distribution density of the brightness of light in interstellar space in the case of several clouds uniformly distributed in the equatorial plane of the Galaxy and having different optical densities

Contribution of copper Nqr spectroscopy to the geological studies of complex sulfides and oxides

Many energy-related areas such as nuclear waste isolation, continental drilling, fossil fuel recovery, and geothermal energy are directly associated with an in-depth understanding of the earth sciences. Of particular interest is the development of analytical techniques which can augment existing ones in developing a better understanding of mineralogy. Presently, available instrumental techniques for studying mineralogical problems such as x-ray, electron and neutron diffraction, nuclear gamma resonance (NGR or Mössbauer spectroscopy), electron microscopy and transmission electron microscopy have inherent limitations. These manifest themselves in being unable to characterize mineral samples fully, especially if they are polycrystalline. Nuclear Quadrupole Resonance (NQR) spectroscopy offers the potential for being able to obtain accurate high resolution spectra. These can then be interpreted to give structural information which can be related to local electronic structure, atomic arrangement, order/disorder phenomena, and crystal phase transformation. In addition, internal dynamics (ionic diffusion, metallic behavior, rotations, and so on) in the solid state can be studied. Furthermore, since NQR data are sensitive to changes in temperature and pressure, there is the possibility of obtaining stress/strain information. As applied to mineralogical and geological problems, NQR can also provide additional information, for example: chemical activity of minerals (genetic and technological aspects) at different hydrothermal conditions, the studies of impurity configurations in ore minerals and their distribution in crystal lattice, and other. This chapter highlights some NQR studies in copper sulfides, which demonstrate how NQR method can contribute to our understanding of geological problems. Examples are taken primarily from author's investigate groups. © 2009 Springer Science+Business Media B.V

Phase transition and anomalous electronic behavior in the layered superconductor CuS probed by NQR

Nuclear quadrupole resonance (NQR) on copper nuclei has been applied for studies of the electronic properties of quasi-two-dimensional (2D) low-temperature superconductor CuS (covellite) in the temperature range of 1.47-290 K. Two NQR signals corresponding to two structural nonequivalent sites of copper, Cu(1) and Cu(2), have been found. The temperature dependences of copper quadrupole frequencies, linewidths, and spin-lattice relaxation rates altogether demonstrate the structural phase transition near 55 K, which is accompanied by transformations of the electronic spectrum not typical for simple metals. The analysis of NQR results and their comparison with literature data show that the valence of copper ions at both sites is intermediate between monovalent and divalent states with the dominance of the former. It has been found that there is a strong hybridization of the Cu(1) and Cu(2) conduction bands at low temperatures, indicating that the charge delocalization between these ions takes place even in 2D regime. On the basis of our data, the occurrence of an energy gap, charge fluctuations, and charge-density waves, as well as the nature of the phase transition in CuS, are discussed. It is concluded that some physical properties of CuS are similar to those of high-temperature superconductors in the normal state. © 2009 The American Physical Society

NQR/NMR and Mössbauer spectroscopy of sulfides: Potential and versatility

Nuclear quadrupole resonance (NQR), nuclear magnetic resonance (NMR) and nuclear gamma-resonance (NGR or Mössbauer Effect) methods are generally described as highly sensitive tools in studies of local electronic structure and symmetry in solid-state materials. This is due to high informativity in electronic structure investigations, high resolution in phase-structural diagnostics (down to nano-scale), possibility to study polycrystalline and complex compounds, and to the non-destructive character of these methods. As applied to Earth sciences, both NQR/NMR and Mössbauer spectroscopy methods contribute to mineralogical material science and mineral physics. Another important aspect is the fact that these methods, as demonstrated recently, belong to unique techniques suitable for on-line bulk mineralogical analysis. This includes remotely operated sensors used with conveyor systems in mining/materials handling and similar applications where real-time data collection/processing provides significant commercial benefits. These developments open new pathways for NQR/NMR and Mössbauer spectroscopy applications. Notably, NQR/NMR and Mössbauer effects are observed primarily on different nuclei-probes but provide similar information about the local properties of materials (hyperfine fields, electric field gradients and relaxation effects). This makes NQR/NMR and Mössbauer methods mutually complementary despite their significant technical differences. This paper includes examples of recent applications of NQR, NMR and Mössbauer spectroscopic tools to studies of copper-, antimony- and iron-containing sulfides, demonstrating how these methods can contribute to an improved understanding of geochemical problems. © 2013 E. Schweizerbart'sche Verlagsbuchhandlung, D-70176 Stuttgart

Phase transition and anomalous electronic behavior in layered dichalcogenide CuS (covellite) probed by NQR

Nuclear quadrupole resonance (NQR) on copper nuclei has been applied for studies of the electronic properties of quasi-two-dimensional low-temperature superconductor CuS (covellite) in the temperature region between 1.47 and 290 K. Two NQR signals corresponding to two non-equivalent sites of copper in the structure, Cu(1) and Cu(2), has been found. The temperature dependences of copper quadrupole frequencies, line-widths and spin-lattice relaxation rates, which so far had never been investigated so precisely for this material, altogether demonstrate the structural phase transition near 55 K, which accompanies transformations of electronic spectrum not typical for simple metals. The analysis of NQR results and their comparison with literature data show that the valence of copper ions at both sites is intermediate in character between monovalent and divalent states with the dominant of the former. It has been found that there is a strong hybridization of Cu(1) and Cu(2) conduction bands at low temperatures, indicating that the charge delocalization between these ions takes place even in 2D regime. Based on our data, the occurrence of energy gap, charge fluctuations and charge-density waves, as well as the nature of phase transition in CuS are discussed. It is concluded that some physical properties of CuS are similar to those of high-temperature superconductors (HTSC) in normal state.Comment: to be publishe

Modeling protein network evolution under genome duplication and domain shuffling

<p>Abstract</p> <p>Background</p> <p>Successive whole genome duplications have recently been firmly established in all major eukaryote kingdoms. Such <it>exponential </it>evolutionary processes must have largely contributed to shape the topology of protein-protein interaction (PPI) networks by outweighing, in particular, all <it>time-linear </it>network growths modeled so far.</p> <p>Results</p> <p>We propose and solve a mathematical model of PPI network evolution under successive genome duplications. This demonstrates, from first principles, that evolutionary conservation and scale-free topology are intrinsically linked properties of PPI networks and emerge from <it>i) </it>prevailing <it>exponential </it>network dynamics under duplication and <it>ii) asymmetric divergence </it>of gene duplicates. While required, we argue that this asymmetric divergence arises, in fact, spontaneously at the level of protein-binding sites. This supports a refined model of PPI network evolution in terms of protein domains under exponential and asymmetric duplication/divergence dynamics, with multidomain proteins underlying the combinatorial formation of protein complexes. Genome duplication then provides a powerful source of PPI network innovation by promoting local rearrangements of multidomain proteins on a genome wide scale. Yet, we show that the overall conservation and topology of PPI networks are robust to extensive domain shuffling of multidomain proteins as well as to finer details of protein interaction and evolution. Finally, large scale features of <it>direct </it>and <it>indirect </it>PPI networks of <it>S. cerevisiae </it>are well reproduced numerically with only two adjusted parameters of clear biological significance (<it>i.e</it>. network effective growth rate and average number of protein-binding domains per protein).</p> <p>Conclusion</p> <p>This study demonstrates the statistical consequences of genome duplication and domain shuffling on the conservation and topology of PPI networks over a broad evolutionary scale across eukaryote kingdoms. In particular, scale-free topologies of PPI networks, which are found to be robust to extensive shuffling of protein domains, appear to be a simple consequence of the conservation of protein-binding domains under asymmetric duplication/divergence dynamics in the course of evolution.</p

Limitations of Gene Duplication Models: Evolution of Modules in Protein Interaction Networks

It has been generally acknowledged that the module structure of protein interaction networks plays a crucial role with respect to the functional understanding of these networks. In this paper, we study evolutionary aspects of the module structure of protein interaction networks, which forms a mesoscopic level of description with respect to the architectural principles of networks. The purpose of this paper is to investigate limitations of well known gene duplication models by showing that these models are lacking crucial structural features present in protein interaction networks on a mesoscopic scale. This observation reveals our incomplete understanding of the structural evolution of protein networks on the module level

Improved homology-driven computational validation of protein-protein interactions motivated by the evolutionary gene duplication and divergence hypothesis

<p>Abstract</p> <p>Background</p> <p>Protein-protein interaction (PPI) data sets generated by high-throughput experiments are contaminated by large numbers of erroneous PPIs. Therefore, computational methods for PPI validation are necessary to improve the quality of such data sets. Against the background of the theory that most extant PPIs arose as a consequence of gene duplication, the sensitive search for homologous PPIs, i.e. for PPIs descending from a common ancestral PPI, should be a successful strategy for PPI validation.</p> <p>Results</p> <p>To validate an experimentally observed PPI, we combine FASTA and PSI-BLAST to perform a sensitive sequence-based search for pairs of interacting homologous proteins within a large, integrated PPI database. A novel scoring scheme that incorporates both quality and quantity of all observed matches allows us (1) to consider also tentative paralogs and orthologs in this analysis and (2) to combine search results from more than one homology detection method. ROC curves illustrate the high efficacy of this approach and its improvement over other homology-based validation methods.</p> <p>Conclusion</p> <p>New PPIs are primarily derived from preexisting PPIs and not invented <it>de novo</it>. Thus, the hallmark of true PPIs is the existence of homologous PPIs. The sensitive search for homologous PPIs within a large body of known PPIs is an efficient strategy to separate biologically relevant PPIs from the many spurious PPIs reported by high-throughput experiments.</p

On a functional differential equation

© 2017, Pleiades Publishing, Ltd.Conditions for the existence and uniqueness of a solution to a problem for a functional differential equation are presented. A special case of this equation is a functional differential equation derived previously by the authors for the distribution density of the brightness of light in interstellar space in the case of several clouds uniformly distributed in the equatorial plane of the Galaxy and having different optical densities

On a functional differential equation

© 2017, Pleiades Publishing, Ltd.Conditions for the existence and uniqueness of a solution to a problem for a functional differential equation are presented. A special case of this equation is a functional differential equation derived previously by the authors for the distribution density of the brightness of light in interstellar space in the case of several clouds uniformly distributed in the equatorial plane of the Galaxy and having different optical densities